Browsersync will open chrome, serve static files (polymer libs) from bower_components folder and
watch src folder. Any changes are going to be automatically pushed to the browser without reloading.
Skip the bower_components folder in all imports:

I have found polymer as a webcomponent library very useful. However, when using it, I found it hard.

And it is mostly a question to the polymer developers, not you:
Let's say, I just want a simple webpage for my microservices. I don't want to use bower (why the hell would I want to install npm and bower and whatever I don't know toolset).

So is there any way to just download a simple release version of polymer, add it to my webproject, and simply use it?

Everything of Polymer is on GitHub. Just download what you need and add it to your project manually. But I strongly recommend using a dependency management tool like bower, it does make your life easier!